Introduction

The purpose of this chapter is to recap some of the ideas that you learned in geometry and trigonometry in earlier grades. You should feel comfortable with the work covered in this chapter before attempting to move onto the Grade 10
Geometry chapter , the Grade 10
Trigonometry chapter or the Grade 10
Analytical Geometry chapter . This chapter revises:

Theorem of Pythagoras which is used to calculate the lengths of sides of a right-angled triangle

Points and lines

The two simplest objects in geometry are
points and
lines .

A point is a coordinate that marks a position in space (on a number line, on a plane or in three dimensions or even more) and is denoted by a dot. Points are usually labelled with a capital letter. Some examples of how points can be represented are shown in
[link] .

A line is a continuous set of coordinates in space and can be thought of as being formed when many points are placed next to each other. Lines can be straight or curved, but are always continuous. This means that there are never any breaks in the lines (if there are, they would be distinct lines denoted separately). The endpoints of lines are labeled with capital letters. Examples of two lines are shown in
[link] .

Examples of some points (labelled
P ,
Q ,
R and
S ) and some lines (labelled
BC and
DE ).

Lines are labelled according to the start point and end point. We call the line that starts at a point
A and ends at a point
B ,
AB . Since the line from point
B to point
A is the same as the line from point
A to point
B , we have that
AB=BA .

When there is no ambiguity (which is the case throughout this text) the length of the line between points
A and
B is also denoted
AB , the same as the notation to refer to the line itself. So if we say
AB=CD we mean that the length of the line between
A and
B is equal to the length of the line between
C and
D .

Note: in higher mathematics, where there might be some ambiguity between when we want refer to the length of the line and when we just want to refer to the line itself, the notation
|AB| is usually used to refer to the length of the line. In this case, if one says
|AB|=|CD| , it means the lengths of the lines are the same, whereas if one says
AB=CD , it means that the two lines actually coincide (i.e. they are the same). Throughout this text, however, this notation will not be used, and
AB=CD ALWAYS implies that the lengths are the same.

A line is measured in
units of length . Some common units of length are listed in
[link] .

Unit of Length

Abbreviation

kilometre

km

metre

m

centimetre

cm

millimetre

mm

Some common units of length and their abbreviations.

Angles

An
angle is formed when two straight lines meet at a point. The point at which two lines meet is known as a
vertex . Angles are labelled with a
^ called a caret on a letter. For example, in
[link] the angle is at
B^ . Angles can also be labelled according to the line segments that make up the angle. For example, in
[link] the angle is made up when line segments
CB and
BA meet. So, the angle can be referred to as
∠CBA or
∠ABC or, if there is no ambiguity (i.e. there is only one angle at
B ) sometimes simply
∠B . The
∠ symbol is a short method of writing angle in geometry.

In this morden time nanotechnology used in many field .
1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc
2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc
3- Atomobile -MEMS, Coating on car etc.
and may other field for details you can check at Google

Azam

anybody can imagine what will be happen after 100 years from now in nano tech world

Prasenjit

after 100 year this will be not nanotechnology maybe this technology name will be change .
maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments

Azam

name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world

Prasenjit

how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?

At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.